Coherent Structures in Shallow Water Jets

Abstract

This paper reports an experimental investigation of a round jet discharging horizontally from a vertical wall into an isothermal body of water confined in the vertical direction by a flat wall on the bottom and a free surface on top. Specifically, this paper focuses on the effects of vertical confinement on the characteristics of large vortical structures. The jet exit velocity was 2.5 m/s, and the exit Reynolds number was 22,500. Experiments were performed at water layer depths corresponding to 15, 10, and 5 times the jet exit diameter (9 mm). The large-scale structures were exposed by performing a proper orthogonal decomposition (POD) analysis of the velocity field obtained using a particle image velocimetry system. Measurements were made on vertical and horizontal planes—both containing the axis of the jet. All fields-of-view were positioned at an axial location in the range 10<x/D<80. The number of modes used for the POD reconstruction of the velocity fields was selected to recover ∼40% of the turbulent kinetic energy. A vortex identification algorithm was then employed to quantify the size, circulation, and direction of rotation of the exposed vortices. A statistical analysis of the distribution of number, size, and strength of the identified vortices was carried out to explore the characteristics of the coherent structures. The results clearly reveal the existence of numerous vortical structures of both rotational senses in the jet flow, and their number generally decreases in the axial direction while their size increases. The size of vortices identified in the vertical plane is restricted by the water depth, while they are allowed to increase in size in the horizontal plane. Moreover, the results show a significant decrease in the number of small vortices for the shallowest case in the horizontal plane, with a corresponding increase in the number of large vortices and a significant increase in their size. This behavior was accompanied with an increase in the vortex circulation in the horizontal plane and a reduction in the circulation in the vertical plane. This is indicative of the dominance of the pairing process due to shallowness. Moreover, the balance between the positive and negative vortices in the vertical plane changed because of the formation of negative (clockwise) vortices near the solid wall at downstream locations.